If the length of the diagonals of an equilateral quadrilateral is 16 cm and 30 cm then find the perimeter of the equilateral quadrilateral
pleasegive answer step by step
Answers
Answer:
Perimeter = 68cm.
Step-by-step explanation:
An equilateral quadrilateral is one with sides of equal length. There are only two kinds of quadrilateral with equal sides: a rhombus, and a square.
Since it is given that the diagonals are different, it has to be a rhombus.
Some properties of Rhombus:
1. All sides are equal
2. Diagonals bisect each other at right angles.
(See the figure for all the properties)
Let O be the point of intersection of diagonals
Consider ∆AOB,
Diagonals BC = 30cm and AC = 16cm
So, AO = AC/2 = 8cm
BO = BC/2 = 15cm
∆AOB is a right triangle, right angled at angle AOB.
Following Pythagoras theorem,
AB² = AO² + BO² = 8² + 15² = 289
AB = √289 = 17cm, which is the side of the rhombus (all sides equal)
Perimeter of a rhombus is 4 × side.
The side is obtained as 17cm.
Hence, Perimeter = 4 × 17 = 68cm.
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